AP Stat Lesson: Type I and Type II Errors

THE EXCEL SPREADSHEET
Type I and Type II Errors (housed on Box.net...is there a better way to do this?)
Directions for the activity contained in the spreadsheet.

SKILLS ADDRESSED
Statistical significance, Confidence Intervals related to hypothesis tests, Type I Error, Type II Error, Power, Alpha, Beta

THE CONTEXT
A factory is producing pharmaceutical grade glass vials.  Quality control engineers are employed to see if the factory is producing items at or below the industry standard of 5% defects.  They conduct a sample of size 100 (Mistake #1: I know this violates np>10, but it turns out that you wind up failing to reject a lot and it leads to a good understanding of Type II error) and determine the proportion of their sample that is defective. (Mistake #2: sampling 100 items and getting a proportion defective of 0.063 defective is impossible.  They will need to round to a whole number of successes when using the graphing calculator.)  Based on the results of this hypothesis test, they will decide if the factory must undergo a quality control review or continue with business as usual.


THE ACTIVITY
1ST PART - CONDUCT THE TEST, DECIDE WHETHER TO REJECT OR FAIL TO REJECT
It's dynamic.  Each kid will receive a randomly generated proportion.  They may do this up to 50 times.
First part of the activity: conduct the one proportion z-test using your graphing calculator.

2ND PART - DECIDE IF YOU MADE THE RIGHT DECISION
Unlock the spreadsheet (password: apstat5).  Have them change the fill color of the "True Proportion" column to reveal the true proportion of items that are actually defective.  They then evaluate their decision as to whether it was correct or incorrect.  Cue a whole class discussion on the 4 different scenarios of errors, then slap the AP Stat vocabulary on.

REFLECTION
Two huge mistakes that led to an amazing understanding of errors.  An overly planned lesson would have avoided these mistakes.  It also would not have generated a discussion on appropriate assumptions and conditions for inference.  An overly planned lesson would have also not brought up the question of "How come I'm failing to reject so much when it's false?"  An awesome comment: "I would not have learned this that well if I didn't have to think about those things."

This was 3 days worth of 46-minute classes.  Let's see how they do on the assessment of these skills.

THE SLIDESHOW

10-11 Errors

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Coming soon to this post...
The Google Form Assessment
A better version of the spreadsheet that allows any null hypothesis and any sample size.
100 comments on how to make this even better (hopefully)